Week 8 - Game theory

Question 1

What does game theory use to study strategic situations?

Answer 1

mathematical models to study strategic situations

Question 2

What are strategic situations based off?

Answer 2

your wellbeing not only depends on your behaviour, it depends on other peoples behaviour

Question 3

What are two market structures use non-strategic situations?

Answer 3

1. Perfect competition (firms price takers, dont have to worry about the prices of their competitors)
2. Monopoly (no competitors to worry about)

Question 4

What market structures use a strategic situation?

Answer 4

Everything in between a Monopoly and Perfect competition

Question 5

What 2 interactions can Game theory be?

Answer 5

cooperative and competitive

Question 6

When can an interaction be ‘cooperative’ in Game theory?

Answer 6

such as when business partners successfully collaborate on a project

Question 7

When can an interaction be ‘competitive’ (or conflicting) in Game theory?

Answer 7

like when two or more firms fight for market share, rival politicians in an election, etc

Question 8

What is Game theory a tool-kit to study?

Answer 8

conflict and cooperation between intelligent and rational decision makers

Question 9

What are the two basic models of Games?

Answer 9

1. Simultaneously played games (Normal form/ Strategic form)
2. Sequentially played games (Extensive form)

Question 10

What are Simultaneously played games (Normal form/ Strategic form)?

Answer 10

the games where the players have to choose their decisions or actions simultaneously

Simultaneous doesnt quite literally mean choosing at the same time, but means that players choose a decision without knowing what others are doing

Question 11

What are sequentially played games (extensive form)?

Answer 11

moves are made sequentially (one after the other)

players can see clearly what moves have been taken so far before they make their own choice

Question 12

What are three elements to a Normal form game?

Answer 12

1. Players
2. Strategies
3. Payoffs/ Utilities

Question 13

What is an example of a Normal form game matrix?

Answer 13

.
Player 2
M N

            X    a_1, a_2          b_1, b_2 Player 1
            Y   c_1, c_2           d_1, d_2

Players - have 2
Strategies - each player have 2

Outcomes - 4 in total (XM, XN, YM, YN)

a_1 represents player 1 payoff
a_2 represents player 2 payoff

Question 14

What is a famous game in Game theory?

Answer 14

The Prisoner’s Dilemma

Question 15

What is a version of the story The Prisoner’s Dilemma?

Answer 15

Two people (1&2) are arrested on charges of a bank robbery (major crime)

*Bad news: Evidence links them together as
collaborators and proves them to be at least
offenders (minor crime)
*Good news: they cannot prove that they are the real robbers, unless one of them confesses
*If one confesses and the other does not, the
confessor benefits from collaborating with the police and gets a lighter sentence

The police keep them in two separate cells
and give each of them the following choices
(Actions/Strategies):
1.Confess (“DEFECT” from the other prisoner)
2.Keep silent (“COOPERATE” with the other
prisoner)
*They are told that both are given the same
choices.
*Both will face the prison terms (Payoffs)
based on their actions

Question 16

Eg1 The Prisoner’s Dilemma Matrix

Answer 16

.
Player 2
Cooperate Defect

Cooperate -1, -1 -4, 0

Player 1

Defect 0, -4 -3,-3

-1 = 1 month

can present with positive numbers

Question 17

How do you solve a game?

Answer 17

Many ways, different economists have many slightly different ways of reaching the same result

Solutions must have the following qualities:
1. The outcome is stable (meaning nobody has an incentive to move from an outcome)
2. The outcome is reached by rational thinking (meaning players are assumed to think in a logical way to maximise their expected payoff

Question 18

What is one of the main methods used to solve a game?

Answer 18

finding the best responses and using this to identify a Nash equilibrium

Question 19

What are 3 approaches to solve a game and find a Nash equilibrium?

Answer 19

1. Dominance
2. Iterated Dominance
3. ?

Question 20

Strict dominance using The Prisoner’s Dilemma Matrix

Answer 20

.
Player 2
Cooperate Defect

Cooperate 4, 4 1, 5

Player 1

Defect 5, 1 2, 2

defect is always better than cooperate as the number is greater than cooperate

Defect, Defect is the Nash equilibrium, payoff 2,2
The outcome is Stable (meaning nobody has an incentive to move from this outcome)

Question 21

What idea does dominance comes from?

Answer 21

that the reason we can delete actions are because other actions for the player exist that is always better

Question 22

What is iterated dominance?

Answer 22

some games exist where actions can be ‘sequentially deleted’ because they are illogical to play if our agent is rational

iterated -> things that happen in ‘iterations’
(occur step by step

Question 23

Eg of Iterated elimination of strictly dominated strategies

Answer 23

.
Player 2
L M R

       U 13,3   1,4    7,3

Pla 1 M 4,1 3,3 6,2

       D -1,9   2,8     8,-1

if rational Player 2 wont choose R
if rational Player 1 wont choose D, M better

if rational Player 2 M dominates L
Player 2 only chooses M

Player 1 wont choose U

then outcome MM 3,3

Question 24

What does battle of the sexes have?

Answer 24

games having more than one Nash equilibrium

Question 25

Examples of Battle of the sexes

Answer 25

You and your partner are planning a belated meal for Valentine’s Day; it’s been agreed that you will cook, whilst your partner will bring the wine. You prefer beef and, naturally, red wine to go with it. Your partner prefers fish and, naturally, white wine to go with it. But you’ve both been really busy, and haven’t had a chance to talk about the meal beforehand Your Partner Red White Beef 4,1 0,0 You Fish 0,0 1,4 if my partner chooses red wine, pick beef (utility 4) if my partner chooses white wine, pick fish (utility 1) vise versa for the partner so has 2 nash equilibrium beef red 4,1 and fish white 1,4 both stable outcome dont want utility of 0

Question 26

What does Matching Pennies have?

Answer 26

Game with no (pure strategy) Nash equilibrium

Question 27

Example of Matching pennies

Answer 27

Players 1 and 2 each put a penny on a table simultaneously. If the two pennies come up the same side (heads or tails) then player 1 gets both; otherwise player 2 does. We can represent this in the following matrix Player 2 H T H 1,-1 -1,1 Pla1 T -1,1 1,-1 if Player 2 chooses H, Player 1 will choose H if Player 2 chooses T, Player 1 will choose T if Player 1 chooses H, Player 2 will choose T if Player 1 chooses T, Player 2 will choose H in every outcome theres only one payoff highlighted, no nash equilibrium also player can change strategy to other one, no stable outcome doesnt have a pure strategy nash equilibrium has a mixed strategy equilibrium

Question 28

What sort of games are normal form games?

Answer 28

one shot games, the interaction happens just once

Question 29

What sort of games are games likely to be in reality?

Answer 29

repeated games, the interaction happens many times or periodically

Question 30

What are 2 types of repeated games?

Answer 30

1. Finitely repeated games 2. Infinitely repeated games

Question 31

What are finitely repeated game?

Answer 31

the same (stage) game that is repeated a finite number of times each prison dilemma is a stage game in this repeated game (including eg 10 prison dilemmas) a stage game looks like a table created before

Question 32

What is an infinitely repeated game?

Answer 32

the same (stage) game that is repeated a infinite number of times infinite amount of strategies

Question 33

What are 2 strategies in infinitely repeated games?

Answer 33

1. Grim trigger 2. Tit for tat

Question 34

What is the grim trigger strategy?

Answer 34

I will first cooperate. But as soon as you defect, I will defect for the remainder of the iterated game.

Question 35

What is the tit for tat strategy?

Answer 35

I will first cooperate, then I will subsequently replicate your previous action. If you previously were cooperative, I am cooperative. If not, I am not. Tit-for-tat has been very successfully used as a strategy for the repeated prisoner's dilemma.

Question 36

What are sequential games?

Answer 36

players who do not make decisions simultaneously, and one player's decision affects the outcomes and decisions of other players like chess

Question 37

What are 2 types of sequential games?

Answer 37

1. Perfect information games 2. Imperfect information games

Question 38

How do we model a sequential game (perfect information game)?

Answer 38

a game tree for an extensive form game (looks like upside down tree) the normal form table doesnt tell you the structure of the story

Question 39

Example of a perfect information game

Answer 39

eg Entry Deterrence Two firms: Potential entrant (player 1) and Incumbent (player 2) The entrant has two choices: Enter or Stay out (of the industry) If entrant stays out, incumbent gets a large profit and entrant gets zero. If the entrant decides to enter, then incumbent must choose whether to accommodate the entrant or enter into a price war. If incumbent starts a price war, then both firms suffer. If incumbent accommodates the entrant, then they both obtain modest profits.

Question 40

What is a backward induction?

Answer 40

starting with the last player's action and moving backward. It effectively determines the Nash equilibrium for each subgame of the game

Question 41

What is assumed in games?

Answer 41

people are selfish

Question 42

What is behavioural game theory?

Answer 42

People are not always self-interested. For example, sometimes they may make decisions based on their social preferences. eg Inequality aversion Kindness reciprocity Guilt aversion People may not always best respond to each other. They may use other reasonings…